Definition 2.1  ([1]}). A finitely additive nonnegative measure \(\mu \)  is called purely finitely additive (pure charge, pure mean) if any countably additive measure \(\lambda \)  satisfying the condition \(0\le \lambda \le \mu \)  is identically zero. An alternating measure \(\mu \)  is called purely finitely additive if both components of its Jordan decomposition \(\mu = \mu ^{+}-\mu ^{-}\)  are purely finitely additive.

